Local grand Lebesgue spaces on quasi-metric measure spaces and some applications

Bibliographic Details
Main Author: Rafeiro, Humberto
Publication Date: 2022
Other Authors: Samko, Stefan, Umarkhadzhiev, Salaudin
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.1/18479
Summary: We introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.
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spelling Local grand Lebesgue spaces on quasi-metric measure spaces and some applicationsGrand Lebesgue spacesMaximal functionSingular integralsRiesz potentialWe introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.SpringerSapientiaRafeiro, HumbertoSamko, StefanUmarkhadzhiev, Salaudin2022-11-09T09:31:31Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/18479eng1385-129210.1007/s11117-022-00915-zinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-18T17:28:03Zoai:sapientia.ualg.pt:10400.1/18479Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T20:23:19.697582Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
spellingShingle Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
Rafeiro, Humberto
Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
title_short Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_full Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_fullStr Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_full_unstemmed Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_sort Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
author Rafeiro, Humberto
author_facet Rafeiro, Humberto
Samko, Stefan
Umarkhadzhiev, Salaudin
author_role author
author2 Samko, Stefan
Umarkhadzhiev, Salaudin
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Rafeiro, Humberto
Samko, Stefan
Umarkhadzhiev, Salaudin
dc.subject.por.fl_str_mv Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
topic Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
description We introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.
publishDate 2022
dc.date.none.fl_str_mv 2022-11-09T09:31:31Z
2022
2022-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.1/18479
url http://hdl.handle.net/10400.1/18479
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1385-1292
10.1007/s11117-022-00915-z
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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